Fluctuation-induced Interaction Research Articles

Fluctuation-Induced Interaction in Turbulent Flows.

Fluctuation-induced forces are observed in numerous physical systems spanning from quantum to macroscopic scale. However, there is as yet no experimental report of their existence in hydrodynamic turbulence. Here, we present evidence of an attraction force mediated via turbulent fluctuations by using two walls locally confining 2D turbulence. This long-range interaction is a function of the wall separation and the energy injection rate in the turbulent flow. As the wall spacing decreases, the confined flow becomes less energetic and more anisotropic in the bounded domain, producing stronger attraction. The mechanism of force generation is rooted in a nontrivial fluid-wall coupling where coherent flow structures are guided by the cavity walls. For the narrowest cavities studied, a resonance phenomenon at the flow forcing scale leads to a complex short-range interaction. The results could be relevant to problems encountered in a range of fields from industrial multiphase flows to modeling of planetary formation.

Field-theoretical approach to the Casimir-like interaction in a one-dimensional Bose gas

We study the fluctuation-induced interaction between two impurities in a weakly interacting one-dimensional Bose gas using the field-theoretical approach. At separations between impurities shorter and of the order of the healing length of the system, the induced interaction has a classical origin and behaves exponentially. At separations longer than the healing length, the interaction is of a quantum origin and scales as the third power of the inverse distance. Finite temperature destroys the quasi-long-range order of the Bose gas and, accordingly, the induced interaction becomes exponentially suppressed beyond the thermal length. We obtain analytical expressions for the induced interaction at zero and finite temperature that are valid at arbitrary distances. We discuss experimental realizations as well as possible formation of bound states of two impurities, known as bipolarons.

Green function approach to fluctuation-induced interaction between polymer chains on membranes

This paper investigates the fluctuation-induced interaction between flexible ideal polymer chains on membranes. Tiny fluctuations happen in the vicinity of the curved surface of the membrane where the potential energy is in the lowest value. The fluctuations are governed by the Helfrich effective surface energy and the effective interaction energy. Under this viewpoint, the energy and the entropy corresponds to one-point and two-point Green function, respectively. The variations of surface energy and the leading-term interaction between chains are calculated with chains anchored to a membrane and strongly confined between two planar membranes in the three dimensional space.

Casimir interaction of rodlike particles in a two-dimensional critical system.

We consider the fluctuation-induced interaction of two thin, rodlike particles, or "needles," immersed in a two-dimensional critical fluid of Ising symmetry right at the critical point. Conformally mapping the plane containing the needles onto a simpler geometry in which the stress tensor is known, we analyze the force and torque between needles of arbitrary length, separation, and orientation. For infinite and semi-infinite needles we utilize the mapping of the plane bounded by the needles onto the half plane, and for two needles of finite length we use the mapping onto an annulus. For semi-infinite and infinite needles the force is expressed in terms of elementary functions, and we also obtain analytical results for the force and torque between needles of finite length with separation much greater than their length. Evaluating formulas in our approach numerically for several needle geometries and surface universality classes, we study the full crossover from small to large values of the separation to length ratio. In these two limits the numerical results agree with results for infinitely long needles and with predictions of the small-particle operator expansion, respectively.

First-order phase transition and tricritical point in multibandU(1)London superconductors

The order of the superconducting phase transition is a classical problem. Single-component type-2 superconductors exhibit a continuous ``inverted-$XY$'' phase transition, as was first demonstrated for $U(1)$ lattice London superconductors by a celebrated duality mapping with subsequent backing by numerical simulations. Here we study this problem in multiband $U(1)$ London superconductors and find evidence that by contrast the model has a tricritical point. The superconducting phase transition becomes first order when the Josephson length is sufficiently large compared to the magnetic field penetration length. We present evidence that the fluctuation-induced dipolar interaction between vortex loops makes the phase transition discontinuous. We discuss that this mechanism is also relevant for the phase transitions in multicomponent gauge theories with higher broken symmetry.

Hydrodynamic fluctuation-induced forces in confined fluids.

We study thermal, fluctuation-induced hydrodynamic interaction forces in a classical, compressible, viscous fluid confined between two rigid, planar walls with no-slip boundary conditions. We calculate hydrodynamic fluctuations using the linearized, stochastic Navier-Stokes formalism of Landau and Lifshitz. The mean fluctuation-induced force acting on the fluid boundaries vanishes in this system, so we evaluate the two-point, time-dependent force correlations. The equal-time correlation function of the forces acting on a single wall gives the force variance, which we show to be finite and independent of the plate separation at large inter-plate distances. The equal-time, cross-plate force correlation, on the other hand, decays with the inverse inter-plate distance and is independent of the fluid viscosity at large distances; it turns out to be negative over the whole range of plate separations, indicating that the two bounding plates are subjected to counter-phase correlations. We show that the time-dependent force correlations exhibit damped temporal oscillations for small plate separations and a more irregular oscillatory behavior at large separations. The long-range hydrodynamic correlations reported here represent a "secondary Casimir effect", because the mean fluctuation-induced force, which represents the primary Casimir effect, is absent.

Fluctuation-induced forces governed by the dielectric properties of water—A contribution to the hydrophobic interaction

The hydrophobic interaction between objects immersed in water is typically attractive and adds to the well-known van der Waals interaction. The former supposedly dominates the latter on nanometric distances and could be of major importance in the assembly of biologic objects. Here, we show that the fluctuation-induced attraction between two objects immersed in a correlated dielectric medium which models water is the sum of a van der Waals term and a short-range contribution that can be identified as part of the hydrophobic interaction. In this framework, we calculate analytically the fluid correlation function and the fluctuation-induced interaction between small and extended inclusions embedded in water and we characterize the hydrophobic terms.

Magnetic-order-driven topological transition in the Haldane-Hubbard model

In this Rapid Communication we study the Haldane model with on-site repulsive interactions at half-filling. We show that the mean-field Hamiltonian with magnetic order effectively modifies parameters in the Haldane Hamiltonian, such as sublattice energy difference and phase in next-nearest hopping. As interaction increases, increasing of magnetic order corresponds to varying these parameters and, consequently, drives topological transitions. At the mean-field level, one scenario is that the magnetic order continuously increases, and, inevitably, the fermion gap closes at the topological transition point. Beyond the mean field, fluctuation-induced interaction can further open up the gap, rendering a first-order transition. Another scenario is a first-order transition at the mean-field level across which a canted magnetic order develops discontinuously, avoiding the fermion gap closing. We find that both scenarios exist in the phase diagram of the Haldane-Hubbard model. Our predication is relevant to recent experimental realization of the Haldane model in cold-atom system.

Surface tension and disjoining pressure of free-standing smectic films above the bulk smectic-A-isotropic transition temperature

We have carried out a numerical study of both the structural and thermodynamic properties of free-standing smectic films for the case of enhanced pair interaction in the bounding layers. Calculations, based upon the extended McMillan's mean-field theory with anisotropic forces, show that the layer-thinning transitions are characterized by abrupt drops to lower values, both for a disjoining pressure and a fluctuation-induced long-range interaction between the smectic film surfaces, and then continues to increase with a larger positive slope. Reasonable agreement between the theoretically predicted and the experimentally obtained data on the surface tension of the partially fluorinated 5-n-alkyl-2-(4-n-(perfluoroalkyl-metheleneoxy)phenyl) film has been obtained.

Pseudo-Casimir interactions across nematic films with disordered anchoring axis

We study the effective pseudo-Casimir interaction forces mediated by a nematic liquid-crystalline film bounded by two planar surfaces, one of which imposes a random (disordered) distribution of the preferred anchoring axis in the so-called easy direction. We consider both the case of a quenched as well as an annealed disorder for the easy direction on the disordered surface and analyze the resultant fluctuation-induced interaction between the surfaces. In the case of quenched disorder, we show that the disorder effects appear additively in the total interaction and are dominant at intermediate inter-surface separations. Disorder effects are shown to be unimportant at both very small and very large separations. In the case of annealed disorder its effects are non-additive in the total inter-surface interaction and can be rationalized in terms of a renormalized extrapolation length.

Casimir interactions in semiflexible polymers

We investigate the Casimir or fluctuation-induced interaction between two cross-linkers bound to the same semiflexible filament. The calculation is complicated by the appearance of second-order derivatives in the bending Hamiltonian for such filaments, which requires a careful evaluation of the the path integral formulation of the partition function in order to arrive at the physically correct continuum limit and properly address ultraviolet divergences. Doing so based on the previous work of Kleinert [Kleinert, J. Math. Phys. 27, 3003 (1986)], we find that cross-linkers interact along a filament with an attractive logarithmic potential proportional to thermal energy. The proportionality constant depends on whether and how the cross-linkers constraint the relative angle between the two filaments to which they are bound. We comment on the implications of this Casimir interaction for equilibrium distribution of labile cross-linkers in semiflexible biopolymer, e.g., F-actin, networks, and bundles.

Three-body fluctuation-induced interaction at fluid interfaces: A strong deviation from the pairwise summation

We present a new method based on the scattering technique to investigate fluctuation-induced forces at a fluid interface. The scattering approach, well suited to the study of many-body systems of arbitrary geometries, is augmented to include boundary fluctuations. Using this method, we study the deviation of the total fluctuation-induced interaction from the sum of pairwise energies for three colloidal particles. We consider both frozen and fluctuating colloids and obtain a very good agreement between analytical and numerical results. We find a marked difference in the three-body fluctuation-induced free energy between the frozen and fluctuating colloids, both in sign and relative size.

Nonadditivity of Fluctuation-Induced Forces in Fluidized Granular Media

We investigate the effective long-range interactions between intruder particles immersed in a randomly driven granular fluid. The effective Casimir-like force between two intruders, induced by the fluctuations of the hydrodynamic fields, can change its sign when varying the control parameters: the volume fraction, the distance between the intruders, and the restitution coefficient. More interestingly, by inserting more intruders, we verify that the fluctuation-induced interaction is not pairwise additive. The simulation results are qualitatively consistent with the theoretical predictions based on mode coupling calculations. These results shed new light on the underlying mechanisms of collective behaviors in fluidized granular media.

QED energy–momentum trace as a force in astrophysics

We study the properties of the trace T of the QED energy–momentum tensor in the presence of quasi-constant external electromagnetic fields. We exhibit the origin of T in the quantum nonlinearity of the electromagnetic theory. We obtain the quantum vacuum fluctuation-induced interaction of a particle with the field of a strongly magnetized compact stellar object.

Fluctuation-Induced Interaction between Randomly Charged Dielectrics

Monopolar charge disorder effects are studied in the context of fluctuation-induced interactions between neutral dielectric slabs. It is shown that quenched bulk charge disorder gives rise to an additive contribution to the net interaction force which decays as the inverse distance between the slabs and may thus completely mask the standard Casimir-van der Waals force at large separations. By contrast, annealed (bulk or surface) charge disorder leads to a net interaction force whose large-distance behavior agrees with the universal Casimir force between ideal conductors, which scales as the inverse cubic distance, and the dielectric properties enter only in the subleading corrections.

“Elastic” fluctuation-induced effects in smectic wetting films

The Li-Kardar field theory approach is generalized to wetting smectic films and the “elastic” fluctuation-induced interaction is obtained between the external flat bounding surface and distorted IA (isotropic liquid-smectic A) interface acting as an “internal” (bulk) boundary of the wetting smectic film under the assumption that the IA interface is essentially “softer” than the surface smectic layer. This field theory approach allows calculating the fluctuation-induced corrections in Hamiltonians of the so-called “correlated” liquids confined by two surfaces, in the case where one of the bounding surfaces is “rough” and with different types of surface smectic layer anchoring. We obtain that in practice, the account of thermal displacements of the smectic layers in a wetting smectic film reduces to the addition of two contributions to the IA interface Hamiltonian. The first, so-called local contribution describes the long-range thermal “elastic” repulsion of the fluctuating IA interface from the flat bounding surface. The second, so-called nonlocal contribution is connected with the occurrence of an “elastic” fluctuation-induced correction to the stiffness of the IA interface. An analytic expression for this correction is obtained.

Finite-Temperature Transition in the Spin-Dimer Antiferromagnet BaCuSi2O6

We consider a classical XY-like Hamiltonian on a body-centered tetragonal lattice, focusing on the role of interlayer frustration. A three-dimensional (3D) ordered phase is realized via thermal fluctuations, breaking the mirror-image reflection symmetry in addition to the XY symmetry. A heuristic field-theoretical model of the transition has a decoupled fixed point in the 3D XY universality, and our Monte Carlo simulation suggests that there is such a temperature region where long-wavelength fluctuations can be described by this fixed point. However, it is shown using scaling arguments that the decoupled fixed point is unstable against a fluctuation-induced biquadratic interaction, indicating that a crossover to nontrivial critical phenomena with different exponents appears as one approaches the critical point beyond the transient temperature region. This new scenario clearly contradicts the previous notion of the 3D XY universality.

Fluctuation-induced interaction in smectic films under an ordering external field

Within a quadratic functional integral approach, we investigate the influence of an external magnetic field in the fluctuation-induced surface–surface interaction of free-standing smectic liquid crystals. We find that the typical 1/ l decay of the Casimir-like contribution to the free-energy of a film with thickness l in the absence of external fields is replaced by a faster 1/ l 2 decay for finite fields. We show the existence of a characteristic thickness delimiting the crossover between these distinct regimes which continuously decreases as stronger fields are considered.

Surface effects on the amplitude of fluctuation-induced interactions in smectic films.

Within a quadratic functional integral approach, we investigate the role played by surface terms in the fluctuation-induced surface-surface interaction of free standing smectic liquid crystals. We show that the typical 1/l decay of the Casimir-type contribution to the free energy of a film with thickness l is replaced by a faster 1/l3 decay at a characteristic surface tension. An intermediate 1/l2 decay can also take place for specific surface parameters with unlike boundary conditions. In all the investigated cases, a repulsive long-range force appears only for mixed boundary conditions with strong anchoring at one surface and weak anchoring at the opposite one. Further, the amplitude of the thermal Casimir energy, besides being influenced by the applied surface tension, depicts a nonmonotonic dependence on the coupling between the outermost film layers, reflecting a crossover between strong and weak anchoring regimes.

Casimir effect in fluids above the isotropic-lamellar transition.

We study fluctuation-induced interaction in confined fluids above the isotropic-lamellar transition. At an ideally continuous transition, the disjoining pressure has the asymptotic form Pi(d-->infinity) approximately -Ck(B)Tq(2)(0)/d, where d is the interwall distance, q(0) is the wave number of the scattering peak, and C = 1/4pi in the strong anchoring limit. The long-rangedness is enhanced due to continuous distribution of soft modes in the q space. An unconventionally strong Casimir force with a range of several lamella thicknesses is realistic above the transition. We also find an oscillatory force profile near a surface-induced transition.